### ?

## Transition Dynamics in a Network Game with Heterogeneous Agents: the Stochastic Case

Automation and Remote Control. 2022. Vol. 13. No. 1. P. 483–501.

Korolev A. V.

Stochastic parameters are introduced into a model of network games with production and knowledge externalities. The model was formulated by V. Matveenko and A. Korolev and generalizes Romer’s two-period model. The agents’ productivities have both deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle that occurs in the process of combining the agents. Explicit expressions for the dynamics of a single agent and dyad agents are obtained in the form of Brownian random processes. Solutions of stochastic equations and systems are analyzed qualitatively.

Volkova O. N., Vologina D.A., Korolev A. V., Automation and Remote Control 2022 Vol. 83 No. 6 P. 960–978

In this paper, stochastic parameters are introduced into the network games model with production and externalities of knowledge. This model was formulated by V. Matveenko and A. Korolev and generalized the two-period Romer model. The agents’ productivities have deterministic and Wiener components. We consider the dynamics that occur when two complete networks are combined. Explicit ...

Added: July 6, 2022

., 2019

In this paper, we consider the following problem - what affects
the Nash equilibrium amount of investment in knowledge when some agents
of the complete graph enter another full one. The solution of this problem will
allow us to understand exactly how game agents will behave when deciding
whether to enter the other net, what conditions and externalities affect it
and ...

Added: September 29, 2019

Matveenko V. D., Korolev A. V., Automation and Remote Control 2019 Vol. 79 No. 7 P. 1342–1360

In each node of a network, economy is described by the simple two-period Romer’s
model of endogenous growth with production and knowledge externalities. The sum of knowledge
levels in the neighbor nodes causes an externality in the production of each node of the
network. The game equilibrium in the network is investigated. The agents’ solutions depending
on the size ...

Added: June 22, 2019

Matveenko V., Korolev A. V., Automation and Remote Control 2019 Vol. 80 No. 3 P. 556–575

This paper considers a network game as follows. In each node of a network, economy
is described by the simple two-period Romer’s model of endogenous growth with production
and knowledge externalities. The sum of knowledge levels in the neighbor nodes causes an
externality in the production of each network node. The concept of node type is introduced
and a ...

Added: June 22, 2019

Switzerland: Springer Publishing Company, 2020

In this paper, we consider the following problem - what affects the Nash equilibrium amount of investment in knowledge when one of the complete graph enters another full one. The solution of this problem will allow us to understand exactly how game agents will behave when deciding whether to enter the other net, what conditions ...

Added: June 23, 2019

Networks Structure, Equilibria, and Adjustment Dynamics in Network Games with Nonhomogeneous Players

Гармаш М. В., Уткина А. А., Korolev A. V., , in : Contributions to Game Theory and Management Volume XII. Vol. XII.: ., 2019. P. 128–139.

In this paper, we consider the following problem - what affects
the Nash equilibrium amount of investment in knowledge when some agents
of the complete graph enter another full one. The solution of this problem will
allow us to understand exactly how game agents will behave when deciding
whether to enter the other net, what conditions and externalities affect it
and ...

Added: September 29, 2019

Matveenko V. D., Korolev A. V., Математическая теория игр и ее приложения 2017 Т. 9 № 3 С. 64–92

Рассматривается игра на сети, в каждом узле которой экономика описывается простой двухпериодной моделью Ромера эндогенного роста с производством и экстерналиями знаний. Сумма уровней знаний в соседних узлах вызывает внешний эффект в производстве каждого узла сети. Вводится понятие типа вершины сети; дается типология сетей в зависимости от типов вершин; показано, что внутренние игровые равновесия определяются указанной ...

Added: November 15, 2017

СПб.: Издательство СЗИУ РАНХиГС, 2018

In this paper, we consider the following problem - what affects the amount of investment in knowledge when one of the network firms enters another innovation network. The solution of this problem will allow us to understand exactly how innovative companies will behave when deciding whether to enter the innovation network of another country or ...

Added: September 15, 2018

Korolev A. V., Garmashov I., , in : Optimization of Complex Systems: Theory, Models, Algorithms and Applications. : Switzerland: Springer Publishing Company, 2020. P. 398–406.

In this paper, we consider the following problem - what affects the Nash equilibrium amount of investment in knowledge when one of the complete graph enters another full one. The solution of this problem will allow us to understand exactly how game agents will behave when deciding whether to enter the other net, what conditions ...

Added: June 23, 2019

Matveenko V. D., Korolev A. V., International Journal of Computational Economics and Econometrics 2017 Vol. 7 No. 4 P. 323–358

We study game equilibria in a network, in each node of which an economy is described by a two-period model of endogenous growth with production and knowledge externalities. Each node obtains an externality produced by the sum of knowledge in neighbour nodes. Uniqueness of the inner equilibrium is proved. Ways of behaviour of agent (passive, ...

Added: October 24, 2017

Matveenko V. D., Гармашов И. А., Гармаш М. В. et al., В кн. : ГОСУДАРСТВО И БИЗНЕС. СОВРЕМЕННЫЕ ПРОБЛЕМЫ ЭКОНОМИКИ. МАТЕРИАЛЫ X Международной научно-практической конференциим 25-27 апреля 2018 года Санкт-Петербург. Материалы международной научно-практической конференции. Том 1. Т. 1.: СПб.: Северо-Западный институт управления РАНХиГС при Президенте РФ, 2018. С. 8–17.

In this paper, we consider the following problem - what affects the amount of investment in knowledge when one of the network firms enters another innovation network. The solution of this problem will allow us to understand exactly how innovative companies will behave when deciding whether to enter the innovation network of another country or ...

Added: September 15, 2018

Matveenko V. D., Korolev A. V., Математическая теория игр и ее приложения 2016 Т. 8 № 1 С. 106–137

Исследуется игровое равновесие в сети, в каждом узле которой экономика описывается простой двухпериодной моделью Ромера эндогенного роста с производством и экстерналиями знаний. Сумма уровней знаний в соседних узлах вызывает внешний эффект в производстве каждого узла сети. Рассматриваются решения агентов в зависимости от получаемой экстерналии. Доказывается единственность внутреннего равновесия. Изучается роль пассивных агентов в формировании сети, ...

Added: April 29, 2016

Gurvich V., Naumova M., Discrete Applied Mathematics 2023 Vol. 340 P. 53–68

In 1975 the first author proved that every finite tight two-person game form g is Nashsolvable,
that is, for every payoffs u and w of two players the obtained normal form game
(g; u,w) has a Nash equilibrium (NE) in pure strategies. Several proofs of this theorem
were obtained later. Here we strengthen the result and give a ...

Added: September 8, 2023

A. A, Gushchin, Urusov M. A., Russian Mathematical Surveys 2019 Vol. 74 No. 5 P. 953–955

We prove that a right-continuous integrable stochastic process admits a minimal embedding in the standard Brownian motion if and only if it is a submartingale or supermartingale. ...

Added: July 20, 2020

Pusev R. S., Theory of Probability and Its Applications 2013 Vol. 57 No. 1 P. 60–81

We find precise small deviation asymptotics for some Brownian functionals in the weighted Hilbert norm without knowing of eigenfunctions of corresponding integral Fredholm operators. As particular cases we find for the first time the small deviation asymptotics of Brownian excursion and Brownian meander. ...

Added: January 30, 2015

Gurvich V., Naumova M., Annals of Operations Research 2023 No. 336 P. 1905–1927

Added: August 7, 2024

Samoylenko I., Кулешов И. В., Райгородский А. М., Компьютерные исследования и моделирование 2023 Т. 15 № 2 С. 355–368

At the middle of the 2000-th, scientists studying the functioning of insect communities identified four basic patterns of the organizational structure of such communities. (i) Cooperation is more developed in groups with strong kinship. (ii) Cooperation in species with large colony sizes is often more developed than in species with small colony sizes. And small-sized ...

Added: July 28, 2023

Pankratova Y., Петросян Л. А., Lecture Notes in Computer Science 2019 Vol. 11548 P. 685–696

In the paper, a two-level infinitely repeated hierarchical game with one player (center) C0 on the first level and S1...Sn subordinate players on the second is considered. On each stage of the game player C0 selects vector x=(x1....xn) from a given set X, in which each component represents a vector of resources delivered by C0 to one of the ...

Added: October 5, 2019

Boros E., Franciosa P. G., Gurvich V. et al., International Journal of Game Theory 2024 Vol. 53 P. 449–473

We prove that a deterministic n-person shortest path game has a Nash equlibrium in
pure and stationary strategies if it is edge-symmetric (that is (u, v) is a move whenever (v, u) is, apart from moves entering terminal vertices) and the length of every
move is positive for each player. Both conditions are essential, though it remains ...

Added: October 31, 2023

Korolev A. V., , in : Frontiers of Dynamic Games Game Theory and Management, St. Petersburg, 2019. : Birkhauser/Springer, 2020. Ch. 6. P. 65–85.

In this paper we introduce stochastic parameters into the network game
model with production and knowledge externalities. This model was proposed
by V. Matveenko and A. Korolev as a generalization of the two-period Romer
model. Agents differ in their productivities which have deterministic and stochastic
(Wiener) components. We study the dynamics of a single agent and the dynamics
of a ...

Added: November 30, 2020

Matveenko V. D., Korolev A. V., Бахтин М. А., В кн. : Математика, статистика и информационные технологии в экономике, управлении и образовании. Ч. 1: Математика и статистика.: Тверь: Тверской государственный университет, 2016. С. 79–84.

This paper studies a model of game interaction on a network with externalities, in which agents choose their levels of investment. We compare two concepts of equilibrium: standard Nash definition and “Jacobian” definition of equilibrium with externalities. It is shown that the equilibrium level of investment is equal to the agent’s alpha centrality. Also, we ...

Added: February 23, 2017

Matveenko V. D., Korolev A. V., Maria O. Zhdanova, International Journal of Engineering Business Management 2017 Vol. 9 P. 1–17

We study game equilibria in a model of production and externalities in network with two types of agents who possess different productivities. Each agent may invest a part of her endowment (it may be, for instance, time or money) in the first of two time periods; consumption in the second period depends on her own ...

Added: September 28, 2017

Matveenko V. D., Korolev A. V., , in : Proceedings of the Fourth Russian Finnish Symposium on Discrete Mathematics. Issue 22.: University of Turku, 2017. P. 119–135.

We study game equilibria in a network, in each node of which an economy is described by a two-period model of endogenous growth with production and knowledge externalities. Each node obtains an externality produced by the sum of knowledge in neighbour nodes. Uniqueness of the inner equilibrium is proved. Ways of behaviour of agent (passive, ...

Added: June 8, 2017

Gurvich V., Naumova M., / Cornell University. Series "Working papers by Cornell University". 2024.

In several recent papers some concepts of convex analysis were extended to discrete sets. This paper is one more step in this direction. It is well known that a local minimum of a convex function is always its global minimum. We study some discrete objects that share this property and provide several examples of convex ...

Added: August 19, 2024